Fast iterative methods for sinc systems

Abstract

We consider linear systems of equations arising from the sinc method of boundary value problems which are typically nonsymmetric and dense. For the solutions of these systems we propose Krylov subspace methods with banded preconditioners. We prove that our preconditioners are invertible and discuss the convergence behavior of the conjugate gradient method for normal equations (CGNE). In particular, we show that the solution of an n-by-n discrete sinc system arising from the model problem can be obtained in O(n log2 n) operations by using the preconditioned CGNE method. Numerical results are given to illustrate the effectiveness of our fast iterative solvers.